Cantor Dust

Also known as the Cantor set, possibly the first pure fractal
ever found – by Georg Cantor around 1872.
To produce Cantor Dust, start with a line segment, divide it in to three
equal smaller segments, take out the middle one, and repeat this process
indefinitely.

Although Cantor Dust is riddled with infinitely many gaps, it still contains
uncountably many points. It has a fractal
dimension of log 2/log 3, or approximately 0.631.